1 26 26 triangle

Acute isosceles triangle.

Sides: a = 1   b = 26   c = 26

Area: T = 12.99875959316
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 2.20438196787° = 2°12'14″ = 0.03884639095 rad
Angle ∠ B = β = 88.89880901607° = 88°53'53″ = 1.5521564372 rad
Angle ∠ C = γ = 88.89880901607° = 88°53'53″ = 1.5521564372 rad

Height: ha = 25.99551918631
Height: hb = 10.9998150717
Height: hc = 10.9998150717

Median: ma = 25.99551918631
Median: mb = 13.01992165663
Median: mc = 13.01992165663

Inradius: r = 0.49904753182
Circumradius: R = 13.00224045131

Vertex coordinates: A[26; 0] B[0; 0] C[0.01992307692; 10.9998150717]
Centroid: CG[8.67330769231; 0.33332716906]
Coordinates of the circumscribed circle: U[13; 0.25500462406]
Coordinates of the inscribed circle: I[0.5; 0.49904753182]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.7966180321° = 177°47'46″ = 0.03884639095 rad
∠ B' = β' = 91.10219098393° = 91°6'7″ = 1.5521564372 rad
∠ C' = γ' = 91.10219098393° = 91°6'7″ = 1.5521564372 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 1 ; ; b = 26 ; ; c = 26 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 1+26+26 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-1)(26.5-26)(26.5-26) } ; ; T = sqrt{ 168.94 } = 13 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13 }{ 1 } = 26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13 }{ 26 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13 }{ 26 } = 1 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 26**2+26**2-1**2 }{ 2 * 26 * 26 } ) = 2° 12'14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1**2+26**2-26**2 }{ 2 * 1 * 26 } ) = 88° 53'53" ; ; gamma = 180° - alpha - beta = 180° - 2° 12'14" - 88° 53'53" = 88° 53'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13 }{ 26.5 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1 }{ 2 * sin 2° 12'14" } = 13 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 26**2 - 1**2 } }{ 2 } = 25.995 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 1**2 - 26**2 } }{ 2 } = 13.019 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 1**2 - 26**2 } }{ 2 } = 13.019 ; ;
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